Solve 3/3+frac{2{2}}+5/11-(3/5-12/20)*frac{123}{456}

$$\frac { 3 } { 3 + \frac { 2 } { 2 } } + \frac { 5 } { 11 } - ( \frac { 3 } { 5 } - \frac { 12 } { 20 } ) \cdot \frac { 123 } { 456 }$$

Evaluate

$$\frac{53}{44}\approx 1.204545455$$

Solution Steps

Divide 2 by 2 to get 1.

$$\frac{3}{3+1}+\frac{5}{11}-\left(\frac{3}{5}-\frac{12}{20}\right)\times \frac{123}{456}$$

Add 3 and 1 to get 4.

$$\frac{3}{4}+\frac{5}{11}-\left(\frac{3}{5}-\frac{12}{20}\right)\times \frac{123}{456}$$

Least common multiple of 4 and 11 is 44. Convert \frac{3}{4} and \frac{5}{11} to fractions with denominator 44.

$$\frac{33}{44}+\frac{20}{44}-\left(\frac{3}{5}-\frac{12}{20}\right)\times \frac{123}{456}$$

Since \frac{33}{44} and \frac{20}{44} have the same denominator, add them by adding their numerators.

$$\frac{33+20}{44}-\left(\frac{3}{5}-\frac{12}{20}\right)\times \frac{123}{456}$$

Add 33 and 20 to get 53.

$$\frac{53}{44}-\left(\frac{3}{5}-\frac{12}{20}\right)\times \frac{123}{456}$$

Reduce the fraction \frac{12}{20} to lowest terms by extracting and canceling out 4.

$$\frac{53}{44}-\left(\frac{3}{5}-\frac{3}{5}\right)\times \frac{123}{456}$$

Subtract \frac{3}{5} from \frac{3}{5} to get 0.

$$\frac{53}{44}-0\times \frac{123}{456}$$

Reduce the fraction \frac{123}{456} to lowest terms by extracting and canceling out 3.

$$\frac{53}{44}-0\times \frac{41}{152}$$

Multiply 0 and \frac{41}{152} to get 0.

$$\frac{53}{44}-0$$

Subtract 0 from \frac{53}{44} to get \frac{53}{44}.

$$\frac{53}{44}$$

Factor

$$\frac{53}{2 ^ {2} \cdot 11} = 1\frac{9}{44} = 1.2045454545454546$$